US8432990B2 - System and method for employing a six-bit rank 1 codebook for four transmit antennas - Google Patents

Abstract

A system and method for employing a six-bit rank 1 codebook for four transmit antennas is provided. A method for communications device operation includes estimating a communications channel between the communications device and a controller serving the communications device, thereby producing a channel estimate, quantizing the channel estimate using a codebook, thereby producing a selected codeword, and transmitting an index corresponding to the selected codeword from the codebook to the controller. The codebook includes a plurality of first level codewords, and each first level codeword includes a plurality of subsidiary codewords.

Description

This application claims the benefit of U.S. Provisional Application No. 61/105,301, filed on Oct. 14, 2008, entitled “Six-Bit Rank 1 Codebook for 4 Transmit Antennas,” which application is hereby incorporated herein by reference.

TECHNICAL FIELD

The present invention relates generally to wireless communications, and more particularly to a system and method for employing a six-bit rank 1 codebook for four transmit antennas.

BACKGROUND

Communication system capacity generally may be significantly improved when the transmitter has full or partial channel state information (CSI). CSI may be obtained by the transmitter via a reverse feedback channel between the transmitter and the receiver. To accommodate the limited feedback channel bandwidth, CSI normally is quantized into digital format at the receiver before feeding back to the transmitter. A codebook based algorithm generally is one of the most efficient ways to quantize the channel. A generic codebook may consist of multiple codewords. In general, the codeword is selected based on certain selection criteria and the corresponding codeword index is fed back from the receiver to the transmitter. The principles for codeword selection may be varied based on different precoding techniques.

A codebook comprises a set of precoding vectors (matrices). At least one of these vectors (matrices), also referred to as codeword, may be chosen by a mobile station (the receiver) and a related feedback message, which can be the codeword itself or its index, will be sent to the base station (the transmitter). The base station may use the vectors (matrices) to help improve the performance of transmissions to the mobile station.

Existing codebooks suffer significant challenges, however, including shortcomings in performance for both correlated and uncorrelated channels, and complexity involved in codeword searching and differential feedback. What is needed, then, is a codebook and method of using same to overcome these disadvantages in the prior art.

SUMMARY OF THE INVENTION

These and other problems are generally solved or circumvented, and technical advantages are generally achieved, by embodiments of a system and method for employing a six-bit rank 1 codebook for four transmit antennas.

In accordance with an embodiment, a method for communications device operation is provided. The method includes estimating a communications channel between the communications device and a controller serving the communications device, thereby producing a channel estimate, quantizing the channel estimate using a codebook, thereby producing a selected codeword, and transmitting an index corresponding to the selected codeword from the codebook to the controller. The codebook has a plurality of first level codewords, and wherein each first level codeword includes a plurality of subsidiary codewords.

In accordance with another embodiment, a method for communications device operation is provided. The method includes estimating a communications channel between the communications device and a controller serving the communications device, thereby producing a channel estimate, performing a first stage quantization of the channel estimate using a codebook, thereby producing a selected first level codeword, and transmitting a first index corresponding to the selected first level codeword from the codebook to the controller. The codebook includes a plurality of first level codewords, each first level codeword has a plurality of subsidiary codewords, and the first stage quantization uses only the plurality of first level codewords. The method also includes performing a second stage quantization of the channel estimate using the codebook, thereby producing a selected codeword, and transmitting a second index corresponding to the selected codeword from the codebook to the controller. The second stage quantization uses the entirety of the codebook.

In accordance with another embodiment, a method for controller operation is provided. The method includes receiving a first channel state information (CSI) from a communications device, reconstructing a first channel estimate using the codebook and the first index, adjusting transmission circuitry in the controller using the reconstructed first channel estimate, and receiving a second CSI from a communications device, wherein the second CSI comprises a second index to a codeword in the codebook. The first CSI includes a first index to a first level codeword in a codebook, the codebook includes a plurality of first level codewords, with each first level codeword having a plurality of subsidiary codewords. The method also includes in response to determining that the first index is different from the second index, reconstructing a second channel estimate using the codebook and the second index, and adjusting transmission circuitry in the controller using the reconstructed second channel estimate. The method further includes transmitting a first transmission to the communications device using the adjusted transmission circuitry.

An advantage of an embodiment is that hierarchical searching of a codebook is supported to reduce codeword searching overhead.

A further advantage of an embodiment is that the codebook is hierarchical in nature, which permits differential feedback, thereby reducing feedback overhead.

Yet another advantage of an embodiment is that good performance is provided for both correlated and uncorrelated communications channels.

The foregoing has outlined rather broadly the features and technical advantages of the present invention in order that the detailed description of the embodiments that follow may be better understood. Additional features and advantages of the embodiments will be described hereinafter which form the subject of the claims of the invention. It should be appreciated by those skilled in the art that the conception and specific embodiments disclosed may be readily utilized as a basis for modifying or designing other structures or processes for carrying out the same purposes of the present invention. It should also be realized by those skilled in the art that such equivalent constructions do not depart from the spirit and scope of the invention as set forth in the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the embodiments, and the advantages thereof, reference is now made to the following descriptions taken in conjunction with the accompanying drawings, in which:

FIG. 1 is a diagram of a wireless communication system;

FIG. 2ais a diagram of a base station;

FIG. 2bis a diagram of a subscriber unit;

FIG. 3ais a flow diagram of subscriber unit operations in providing channel state information to a base station;

FIG. 3bis a flow diagram of subscriber unit operations in quantizing a channel estimate using a codebook;

FIG. 3cis a flow diagram of subscriber unit operations in a first stage of a two-stage quantization of a channel estimate using a codebook;

FIG. 3dis a flow diagram of subscriber unit operations in a second stage of a two-stage quantization of a channel estimate using a codebook;

FIG. 4ais a flow diagram of base station operations in transmitting information to a subscriber unit; and

FIG. 4bis a flow diagram of base station operations in transmitting information to a subscriber unit, wherein the BS receives CSI from the subscriber unit in two stages.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The making and using of the embodiments are discussed in detail below. It should be appreciated, however, that the present invention provides many applicable inventive concepts that can be embodied in a wide variety of specific contexts. The specific embodiments discussed are merely illustrative of specific ways to make and use the invention, and do not limit the scope of the invention.

The embodiments will be described in a specific context, namely a MIMO wireless communications system that makes use of channel state information to improve overall system efficiency. The MIMO wireless communications may be single-user (SU-MIMO) or multi-user (MU-MIMO) and may be compliant with any of a variety of technical standards, such as Long Term Evolution (LTE), LTE-Advanced, WiMAX, IEEE 802.16, and so forth.

FIG. 1 illustrates awireless communication system100.Wireless communications system100 includes a base station (BS)101 and a plurality ofsubscriber units105, which may be mobile or fixed.BS101 andsubscriber units105 communicate using wireless communication. BS may also be referred to as base transceiver stations, Node Bs, enhanced Node Bs, and so forth, while subscriber units may also be referred to as mobile stations, terminals, mobile devices, user equipment, and the like.

BS101 has a plurality oftransmit antennas115 whilesubscriber units105 have one or more receiveantennas110. BS101 sends control information and data tosubscriber units105 through a downlink (DL)channel120 whilesubscriber units105 send control information and data toBS101 through uplink (UL)channel125.

Subscriber units105 may send control information (including channel state information (CSI)) onuplink channel125 to improve the quality of the transmission ondownlink channel120. BS101 may send control information ondownlink channel120 for the purpose of improving the quality ofuplink channel125. Acell130 is a conventional term for the coverage area ofBS101. It is generally understood that inwireless communication system100 there may be multiple cells corresponding to multiple BSs.

In order to reduce control information overhead,subscriber unit105 may quantize the CSI. For example, instead of sending the CSI as analog values,subscriber unit105 may quantize the analog values to a specified number of bits, such as two, three, four, five, and so forth, and transmit the quantized CSI toBS101.

To further reduce control information overhead,subscriber unit105 may use a codebook and transmit an index to a codeword in the codebook in place of the quantized CSI toBS101. The index fedback toBS101 represents a codeword in the codebook that is closest to the quantized CSI.

Since only the index is fedback toBS101, the codebook must be known by bothBS101 andsubscriber units105. The codebook may be pre-specified and stored inBS101 andsubscriber units105 for subsequent use. Alternatively, the codebook may be provided tosubscriber units105 whensubscriber units105 attaches toBS101. In yet another alternative, the codebook may be periodically provided tosubscriber units105. In a further alternative, the codebook may be provided to bothBS101 andsubscriber units105, either at initialization or periodically.

FIG. 2aillustrates aBS201.Data200, in the form of bits, symbols, or packets for example, destined for a plurality of subscriber units being served are sent to ascheduler204, which decides which subscriber units will transmit in a given time/frequency opportunity. Data from subscriber units selected for transmission are processed by modulation andcoding block210 to convert to transmitted symbols and add redundancy for the purpose of assisting with error correction or error detection. The modulation and coding scheme is chosen based in part on information about the channelquality information feedback215.

The output of modulation andcoding block210 is passed to a transmitbeamforming block220, which maps the modulated and coded stream for each subscriber unit onto a beamforming vector. The beamformed outputs are coupled toantennas115 through RF circuitry. The transmit beamforming vectors are input fromsingle user block225 ormulti-user block230. Either beamforming for a single user or multi-user beamforming may be employed, as determined byswitch235, based on information fromscheduler204 and channelquality information feedback215. Part of each subscriber units' channel quality information feedback includes a new feedback message that provides indices corresponding to quantized channel information as described in the embodiments.

Reconstruction block202 uses the indices in channelquality information feedback215 combined with acodebook205 to reconstruct a high-resolution estimate of the quantized channel state information (CSI). The output ofreconstruction block202 is passed to switch235 that forwards the information to either thesingle user block225 or themulti-user block230. Other information may also be passed to these blocks, for example a SINR estimate may be passed to themulti-user block230 to improve its performance.Single user block225 uses the output ofreconstruction block202 as the beamforming vector for the selected user.

Multi-user block230 combines the codeword and other information from multiple users to derive the transmit beamforming vectors employed for each subscriber unit. It may use any number of algorithms known in the literature including zero forcing, coordinated beamforming, minimum mean squared error beamforming, or lattice reduction aided precoding, for example.

Scheduler204 may use any of the known scheduling disciplines in the literature including round robin, maximum sum rate, proportional fair, minimum remaining processing time, or maximum weighted sum rate; generally scheduling decisions are based on channelquality information feedback215 received from the plurality of subscriber units.Scheduler204 may decide to send information to a single subscriber unit via transmit beamforming or may decide to serve multiple subscriber units simultaneously through multiuser MIMO communication.

Modulation andcoding block210 may perform any number of coding and modulation techniques including quadrature amplitude modulation, phase shift keying, frequency shift keying, differential phase modulation, convolutional coding, turbo coding, bit interleaved convolutional coding, low density parity check coding, fountain coding, or block coding. The choice of modulation and coding rate in a preferred embodiment is made based on channelquality information feedback215 in a preferred embodiment and may be determined jointly inscheduler204.

While not explicitly illustrated, it is obvious to those of ordinary skill in the art that OFDM modulation can be used. Further, any number of multiple access techniques could be used including orthogonal frequency division multiple access; code division multiple access; frequency division multiple access; or time division multiple access. The multiple access technique may be combined with the modulation andcoding block210 or the transmitbeamforming block220 among others.

Channelquality information feedback215 may, for purposes of illustration, be in the form of quantized channel measurements, modulation, coding, and/or spatial formatting decisions, received signal strength, and signal-to-interference-plus-noise measurements.

FIG. 2billustratessubscriber unit203.Subscriber unit203 may have one or more receiveantennas110, connecting through RF circuitry to a receiversignal processing block250. Some of the key functions performed by receiversignal processing block250 includechannel estimation block255,estimate SINR block260, and amobility estimate block265.

Channel state information is quantized using aquantization block270 as described in the embodiments. Quantization block270 quantizes the received signal to acodebook275. An index fromcodebook275 may be output fromquantization block270. An estimate of the amount of channel variation, produced bymobility estimate block265, may be used to improve the quantization algorithm by initializing the algorithm from a previous quantization level or adjusting the amount of localization.

Feedback block280 generates a new feedback message by combining the codebook indices output fromquantization block270. Generate channelquality information block285 generates a special feedback control message employing the outputs offeedback block280 to produce channelquality information feedback215.

Channel estimation block255 may employ any number algorithms known in the art including least squares, maximum likelihood, maximum a postiori, Bayes estimator, adaptive estimator, or a blind estimator. Some algorithms exploit known information inserted into the transmit signal in the form of training signals, training pilots, while others use structure in the transmitted signal such as cyclostationarity to estimate coefficients of the channel between the BS and the subscriber unit.

Estimate SINR block260 outputs some measure of performance corresponding to the desired signal. In one embodiment this consists of a received signal power to interference plus noise estimate. In another embodiment, it provides an estimate of the received signal-to-noise ratio. In yet another embodiment, it provides an estimate of the average received signal power, averaged over subcarriers in an OFDM system.

FIG. 3aillustrates a flow diagram ofsubscriber unit operations300 in providing CSI to a BS.Subscriber unit operations300 may be indicative of operations occurring in a subscriber unit, such assubscriber unit203, as the subscriber unit provides CSI to a BS, such asBS201.Subscriber unit operations203 may occur periodically while the subscriber unit is in a normal operating mode after the subscriber unit has become attached to the BS.Subscriber unit operations300 may continue for as long as the subscriber unit remains attached to the BS. In an alternative embodiment,subscriber unit operations300 may occur after the subscriber unit receives a message from the BS indicating that the subscriber unit should provide CSI to the BS.

Subscriber unit operations300 may begin with the subscriber unit estimating a communications channel between itself and the BS that is serving it to produce a channel estimate (block305). After estimating the channel, the subscriber unit may then quantize the channel estimate using a codebook (block310). The channel estimate may be normalized prior to being quantized. The subscriber unit may then transmit an index corresponding to the quantized channel estimate (i.e., the codeword) to the BS (block315).Subscriber unit operations300 may then terminate.

FIG. 3billustrates a flow diagram ofsubscriber unit operations325 in quantizing a channel estimate using a codebook.Subscriber unit operations325 may be indicative of operations occurring in a subscriber unit, such assubscriber unit203, as the subscriber unit provides CSI to a BS, such asBS201.Subscriber unit operations325 may occur each time that the subscriber unit provides CSI to the BS, which may occur periodically or on command from the BS.Subscriber unit operations325 may be an implementation ofblock310 ofFIG. 3a, quantizing a channel estimate using a codebook.

Subscriber unit operations325 may begin after the subscriber unit has estimated the communications channel between itself and the BS that is serving it. With the channel estimate, the subscriber unit may search among a first level of codewords in the codebook for a codeword that maximizes |HW_i|, iε[1, . . . , # codewords], where H is a channel matrix, and W_iare codewords of codebook W (block330).

For example, let W be a codebook of 64 codewords and is expressible as W=D×[W₁; . . . ; W₆₄], in which D is the phase rotation diagonal matrix and given by:

$D=\left[\begin{array}{cccc}{e}^{{\mathrm{j\theta }}_1}& 0& \dots & 0\\ 0& e^{j{\theta }_2}& \ddots & ⋮\\ ⋮& \ddots & \ddots & 0\\ 0& \dots & 0& e^{{\mathrm{j\theta }}_{64}}\end{array}\right],$
where
θ_iε[0,2π),iε[1, . . . , 64]

Let a codeword W_iin codebook W be expressible as:
W_4i+j=U_iK^Hz_j, iε[0, . . . ,15], jε[1, . . . ,4],
where Z=[z₁, z₂, z₃, z₄] and K=[z₁, k₂, k₃, k₄] are two 4×4 unitary matrices, Z_jis the j-th column of Z. Matrices Z and K do not have to be identical. C=[c₁, . . . , c₁₆] is a 4×16 matrix, where c_i, iε[1, . . . , 16] is 4×1 vector, and U_iis a 4×4 unitary matrix denoted by U_i=[c_i, u_i2, u_i3, u_i4].

Additional detail on codebook W and codeword W_iis provided below.

With codebook W as defined above, the first level of codewords in codebook W are codewords [W₁, W₅, W₉, W₁₃, W₁₇, W₂₁, W₂₅, W₂₉, W₃₃, W₃₇, W₄₁, W₄₅, W₄₉, W₅₃, W₅₇, W₆₁]. In general, the first level of codewords may be denoted W_4k+1, kε[0, . . . , 15]. Without loss of generality, assume that |HW₁|≧|HW₂|≧ . . . ≧|HW₆₁|.

It is defined that the subsidiary codewords of the codeword W_4k+1, kε[0, . . . , 15] are [W_4k+2, W_4k+3, W_4k+4]. Inblock330, the codewords corresponding to M the largest |HW_4k+1| are denoted by [W₁, W₅, . . . , W_4M+1]. Consequently, their corresponding subsidiary codewords are searched.

After selecting a codeword from the first level of codewords in codebook W that maximizes |HW_i|, iε[1, . . . , 64] or |HW_i|, iε[1, . . . , # first level codewords], the subscriber unit may search in the subsidiary codewords of the codeword that maximized |HW_i|, iε[1, . . . , 64] or |HW_i|, iε[1, . . . , # subsidiary codewords] (block335). For example, if W₂₉maximizes |HW_i|, iε[1, . . . , 64], then the subsidiary codewords of W₂₉, namely W₃₀, W₃₁, and W₃₂will be searched.

The codeword that is selected as the quantized version of the channel estimate, i.e., either the codeword from the first level of codewords or one of its three subsidiary codewords, is the codeword that maximizes |HW_i|, iε[1, . . . , 64] (block340). In an embodiment, if the codeword from the first level of codewords and one of its subsidiary codeword substantially equally maximizes |HW_i|, iε[1, . . . , 64], then the codeword from the first level of codewords is selected. In an alternate embodiment, the codeword is selected at random if more than one codeword substantially equally maximizes |HW_i|, iε[1, . . . , 64].Subscriber unit operations325 may then terminate.

The quantization of the channel estimate may also occur in two-stages. In a first stage a potentially sub-ideal quantization of the channel estimate may be obtained and in a second stage a potentially ideal quantization of the channel estimate may be obtained. An advantage of the two-stage quantization is that a quick but potentially sub-ideal quantization of the channel estimate may be obtained and made available for use, then at a later time, a potentially better quantization may be obtained.

FIG. 3cillustrates a flow diagram ofsubscriber unit operations350 in a first stage of a two-stage quantization of a channel estimate using a codebook.Subscriber unit operations350 may be indicative of operations occurring in a subscriber unit, such assubscriber unit203, as the subscriber unit provides CSI to a BS, such asBS201.Subscriber unit operations350 may occur each time that the subscriber unit provides CSI to the BS, which may occur periodically or on command from the BS.Subscriber unit operations350 may be an implementation ofblock310 ofFIG. 3a, quantizing a channel estimate using a codebook.

Subscriber unit operations350 may begin with the subscriber unit searching among a first level of codewords in the codebook for a codeword that maximizes |HW_i|, iε[1, . . . , # codewords] (block355). The subscriber unit may then select the codeword in the first level of codewords that maximizes |HW_i|, iε[1, . . . , # codewords] as a first-stage quantization of the channel estimate (block360).Subscriber unit operations350 may then terminate.

FIG. 3dillustrates a flow diagram ofsubscriber unit operations375 in a second stage of a two-stage quantization of a channel estimate using a codebook.Subscriber unit operations375 may be indicative of operations occurring in a subscriber unit, such assubscriber unit203, as the subscriber unit provides CSI to a BS, such asBS201.Subscriber unit operations375 may occur each time that the subscriber unit provides CSI to the BS, which may occur periodically or on command from the BS.Subscriber unit operations375 may be an implementation ofblock310 ofFIG. 3a, quantizing a channel estimate using a codebook.

Subscriber unit operations375 may begin with the subscriber unit searching in the subsidiary codewords of the codeword in the first level of codewords that maximizes |HW_i|, iε[1, . . . , # codewords] for a codeword that maximizes |HW_i|, iε[1, . . . , # codewords] (block380). The subscriber unit may include in its search the codeword in the first level of codewords that maximizes |HW_i|, iε[1, . . . , # codewords]. The subscriber unit may then select the codeword that maximizes |HW_i|, iε[1, . . . , # codewords] out of the first level of codewords that maximizes |HW_i|, iε[1, . . . , # codewords] and its subsidiary codewords as a second-stage quantization of the channel estimate (block385).Subscriber unit operations375 may then terminate.

FIG. 4aillustrates a flow diagram ofBS operations400 in transmitting information to a subscriber unit.BS operations400 may be indicative of operations occurring in a BS, such asBS201, as the BS receives CSI from a subscriber unit, such assubscriber unit203, and makes use of the received CSI to improve the performance of transmissions to the subscriber unit.BS operations400 may occur periodically, when the BS detects that a metric of transmission performance, such as an error rate (e.g., bit-error rate, frame error rate, packet error rate, and so forth) has reached a threshold, when the BS has a transmission to make to the subscriber unit, or so on.

BS operations400 may begin with the BS receiving feedback information from the subscriber unit (block405). The feedback information may include quantized CSI. The quantized CSI comprises an index to a codebook, wherein the index corresponds to a codeword in the codebook that most closely matches a channel estimate of a communications channel between the BS and the subscriber unit. According to an embodiment, the codeword is a codeword from the codebook that maximizes the relationship |HW_i|, iε[1, . . . , # codewords], where H is a channel matrix, and W_iare codewords of the codebook.

The BS extracts the index from the feedback information (block410) and reconstructs the channel estimate vector using the codeword from the codebook that corresponds to the index (block415). As stated previously, both the BS and the subscriber unit have copies of the same codebook. The BS may then use the reconstructed channel estimate vector to adjust radio frequency (RF) hardware in the BS (block420). The BS may make use of the adjusted RF hardware to transmit to the subscriber unit (block425).BS operations400 may then terminate.

FIG. 4billustrates a flow diagram ofBS operations400 in transmitting information to a subscriber unit, wherein the BS receives CSI from the subscriber unit in two stages.BS operations450 may be indicative of operations occurring in a BS, such asBS201, as the BS receives CSI from a subscriber unit, such assubscriber unit203, and makes use of the received CSI to improve the performance of transmissions to the subscriber unit.BS operations450 may occur periodically, when the BS detects that a metric of transmission performance, such as an error rate (e.g., bit-error rate, frame error rate, packet error rate, and so forth) has reached a threshold, when the BS has a transmission to make to the subscriber unit, or so on.

BS operations450 may begin with the BS receiving feedback information from the subscriber unit (block455). The feedback information may include quantized CSI. The quantized CSI comprises a first index to the codebook, wherein the first index corresponds to a first level codeword in the codebook that most closely matches a channel estimate of a communications channel between the BS and the subscriber unit. According to an embodiment, the codeword is a codeword from the codebook that maximizes the relationship |HW_i|, iε[1, . . . , # codewords], where H is a channel matrix, and W_iare codewords of the codebook.

The BS extracts the first index from the feedback information (block457) and reconstructs the channel estimate vector using the codeword from the codebook that corresponds to the first index (block459). As stated previously, both the BS and the subscriber unit have copies of the same codebook. The BS may then use the reconstructed channel estimate vector to adjust radio frequency (RF) hardware in the BS (block461). In an optional step, the BS may make use of the adjusted RF hardware to transmit to the subscriber unit (block463).

The BS receives additional feedback information from the subscriber unit (block465). The feedback information may include quantized CSI. The quantized CSI comprises a second index to the codebook, wherein the second index corresponds to a first level codeword in the codebook or one of its subsidiary codeword that most closely matches a channel estimate of a communications channel between the BS and the subscriber unit. According to an embodiment, the codeword is a codeword from the codebook that maximizes the relationship |HW_i|, iε[1, . . . , # codewords], where H is a channel matrix, and W are codewords of the codebook.

The BS extracts the second index from the feedback information (block467) and if the codeword corresponding to the second index is equal to the codeword corresponding to the first index, the BS transmits to the subscriber unit (block471) andBS operations450 may terminate.

If the codeword corresponding to the second index is different from the codeword corresponding to the first index, the BS reconstructs the channel estimate vector using the codeword from the codebook that corresponds to the second index (block473). The BS may then use the reconstructed channel estimate vector to adjust radio frequency (RF) hardware in the BS (block475). The BS may make use of the adjusted RF hardware to transmit to the subscriber unit (block471) andBS operations450 may terminate.

According to a preferred embodiment, the codebook discussed above may be a six-bit Rank 1 codebook for use in wireless communications systems with subscriber units using up to four transmit antennas. The codebook also features a hierarchical structure to simplify codeword searching and facilitate differential feedback.

The codebook comprises 64 codewords and is denoted by W=D×[W₁; . . . ; W₆₄], in which D is the phase rotation diagonal matrix and given by:

$D=\left[\begin{array}{cccc}{e}^{{\mathrm{j\theta }}_1}& 0& \dots & 0\\ 0& e^{{\mathrm{j\theta }}_2}& \ddots & ⋮\\ ⋮& \ddots & \ddots & 0\\ 0& \dots & 0& e^{{\mathrm{j\theta }}_{64}}\end{array}\right],$
where
θ_iε[0,2π),iε[1, . . . , 64].

A codeword in the codebook may be expressible as:
W_4i+j=U_iK^Hz_j, iε[0, . . . ,15], jε[1, . . . ,4],
where Z=[z₁, z₂, z₃, z₄] and K=[z₁, k₂, k₃, k₄] are two 4×4 unitary matrices, Z_jis the j-th column of Z. Matrices Z and K do not have to be identical. C=[c₁, . . . , c₁₆] is a 4×16 matrix, where c_i, iε[1, . . . , 16] is 4×1 vector, and U_iis a 4×4 unitary matrix denoted by U_i=[c_i, u_i2, u_i3, u_i4].

Matrix C is specified as follows:

C1	0.5000	−0.5000	0.5000	−0.5000
C2	−0.5000	−0.5000	0.5000	0.5000
C3	−0.5000	0.5000	0.5000	−0.5000
C4	0.5000	−0.5000I	0.5000	−0.5000I
C5	−0.5000	−0.5000I	0.5000	0.5000I
C6	−0.5000	0.5000I	0.5000	−0.5000I
C7	0.5000	0.5000	0.5000	−0.5000
C8	0.5000	−0.5000I	−0.5000	−0.5000I
C9	0.5000	−0.5000	0.5000	0.5000
C10	0.5000	0.5000I	−0.5000	0.5000I
C11	0.5000	0.3536 + 0.3536I	0.5000I	−0.3536 + 0.3536I
C12	0.5000	0.3536 − 0.3536I	−0.5000I	−0.3536 − 0.3536I
C13	0.5000	−0.3536 − 0.3536I	0.5000I	0.3536 − 0.3536I
C14	0.5000	−0.3536 + 0.3536I	−0.5000I	0.3536 + 0.3536I
C15	0.5000	0.5000	0.5000	0.5000
C16	0.5000	0.5000I	0.5000	0.5000I

Matrices Z and K are specified as follows:

$Z=K=\left[\begin{array}{cccc}-0.5& -0.5& 0.5j& -0.5j\\ 0.5j& 0.5j& -0.5& 0.5\\ 0.5j& -0.5j& -0.5& -0.5\\ 0.5& -0.5& -0.5j& -0.5j\end{array}\right].$

Matrix U is specified as follows:

$\begin{array}{cc}{U}_1=\left[\begin{array}{cccc}0.5& -0.5& -0.5& 0.5\\ -0.5& -0.5& 0.5& 0.5\\ 0.5& 0.5& 0.5& 0.5\\ -0.5& 0.5& -0.5& 0.5\end{array}\right]& \\ U_2=\left[\begin{array}{cccc}-0.5& -0.5& 0.5& 0.5\\ -0.5& 0.5& 0.5& -0.5\\ 0.5& 0.5& 0.5& 0.5\\ 0.5& -0.5& 0.5& -0.5\end{array}\right]& \\ U_3=\left[\begin{array}{cccc}-0.5& 0.5& 0.5& -0.5\\ 0.5& 0.5& -0.5& -0.5\\ 0.5& 0.5& 0.5& 0.5\\ -0.5& 0.5& -0.5& 0.5\end{array}\right]& \\ U_4=\left[\begin{array}{cccc}0.5& -0.5& -0.5& 0.5\\ -0.5j& -0.5j& 0.5j& 0.5j\\ 0.5& 0.5& 0.5& 0.5\\ -0.5j& 0.5j& -0.5j& 0.5j\end{array}\right]& \\ U_5=\left[\begin{array}{cccc}-0.5& -0.5& 0.5& 0.5\\ -0.5j& 0.5j& 0.5j& -0.5j\\ 0.5& 0.5& 0.5& 0.5\\ 0.5j& -0.5j& 0.5j& -0.5j\end{array}\right]& \\ U_6=\left[\begin{array}{cccc}-0.5& 0.5& 0.5& -0.5\\ 0.5j& 0.5j& -0.5j& -0.5j\\ 0.5& 0.5& 0.5& 0.5\\ -0.5j& 0.5j& -0.5j& 0.5j\end{array}\right]& \\ U_7=\left[\begin{array}{cccc}0.5& 0.5& -0.5& -0.5\\ 0.5& -0.5& -0.5j& 0.5j\\ 0.5& 0.5& 0.5& 0.5\\ 0.5& -0.5& 0.5j& -0.5j\end{array}\right]& \\ U_8=\left[\begin{array}{cccc}0.5& 0.5& -0.5& -0.5\\ 0.5j& -0.5j& -0.5& 0.5\\ 0.5& 0.5& 0.5& 0.5\\ 0.5j& -0.5j& 0.5& -0.5\end{array}\right]& \\ U_9=\left[\begin{array}{cccc}0.5& 0.5& 0.5& 0.5\\ 0.5& -0.5j& -0.5& 0.5j\\ 0.5& -0.5& 0.5& -0.5\\ -0.5& -0.5j& 0.5& 0.5j\end{array}\right]& \\ U_{10}=\left[\begin{array}{cccc}0.5& 0.5& 0.5& 0.5\\ -0.5j& -0.5& 0.5j& 0.5\\ -0.5& 0.5& -0.5& 0.5\\ -0.5j& 0.5& 0.5j& -0.5\end{array}\right]& \\ U_{11}=\left[\begin{array}{cccc}0.5& 0.5& 0.5& 0.5\\ -0.5& 0.5j& 0.5& -0.5j\\ 0.5& -0.5& 0.5& -0.5\\ 0.5& 0.5j& -0.5& -0.5j\end{array}\right]& \\ U_{12}=\left[\begin{array}{cccc}0.5& 0.5& 0.5& 0.5\\ 0.5j& 0.5& -0.5j& -0.5\\ -0.5& 0.5& -0.5& 0.5\\ 0.5j& -0.5& -0.5j& 0.5\end{array}\right]& \\ U_{13}=\left[\begin{array}{cccc}0.5& 0.5& 0.5& 0.5\\ \sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j\\ 0.5j& -0.5j& 0.5j& -0.5j\\ -\sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j\end{array}\right]& \\ U_{14}=\left[\begin{array}{cccc}0.5& 0.5& 0.5& 0.5\\ \sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j\\ -0.5j& 0.5j& -0.5j& 0.5j\\ -\sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j\end{array}\right]& \\ U_{15}=\left[\begin{array}{cccc}0.5& 0.5& 0.5& 0.5\\ -\sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j\\ 0.5j& -0.5j& 0.5j& -0.5j\\ \sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j\end{array}\right]& \\ U_{16}=\left[\begin{array}{cccc}0.5& 0.5& 0.5& 0.5\\ -\sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j\\ -0.5j& 0.5j& -0.5j& 0.5j\\ \sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j\end{array}\right].& \end{array}$

From the above definitions of matrices C, Z, K and U_i, the codewords [W₁, . . . , W₆₄] of the codebook W with four place precision is expressible as:

W1	0.5000	−0.5000	0.5000	−0.5000
W2	0.2570 + 0.1701i	−0.6097 − 0.1826i	0.2570 − 0.1701i	−0.6097 + 0.1826i
W3	0.3527 − 0.4396i	0.4271i	−0.3527 − 0.4396i	0 + 0.4271i
W4	−0.1701 + 0.2570i	−0.1826 − 0.6097i	0.1701 + 0.2570i	0.1826 − 0.6097i
W5	−0.5000	−0.5000	0.5000	0.5000
W6	−0.6097 − 0.1826i	−0.2570 − 0.1701i	0.2570 − 0.1701i	0.6097 − 0.1826i
W7	0 + 0.4271i	−0.3527 + 0.4396i	−0.3527 − 0.4396i	−0.4271i
W8	−0.1826 − 0.6097i	0.1701 − 0.2570i	0.1701 + 0.2570i	−0.1826 + 0.6097i
W9	−0.5000	0.5000	0.5000	−0.5000
W10	−0.2570 − 0.1701i	0.6097 + 0.1826i	0.2570 − 0.1701i	−0.6097 + 0.1826i
W11	−0.3527 + 0.4396i	0 − 0.4271i	−0.3527 − 0.4396i	0.4271i
W12	0.1701 − 0.2570i	0.1826 + 0.6097i	0.1701 + 0.2570i	0.1826 − 0.6097i
W13	0.5000	−0.5000i	0.5000	−0.5000i
W14	0.2570 + 0.1701i	0.1826 − 0.6097i	0.2570 − 0.1701i	−0.1826 − 0.6097i
W15	0.3527 − 0.4396i	−0.4271	−0.3527 − 0.4396i	−0.4271
W16	−0.1701 + 0.2570i	0.6097 − 0.1826i	0.1701 + 0.2570i	0.6097 + 0.1826i
W17	−0.5000	−0.5000i	0.5000	0.5000i
W18	−0.6097 − 0.1826i	0.1701 − 0.2570i	0.2570 − 0.1701i	0.1826 + 0.6097i
W19	0.4271i	−0.4396 − 0.3527i	−0.3527 − 0.4396i	0.4271
W20	−0.1826 − 0.6097i	0.2570 + 0.1701i	0.1701 + 0.2570i	−0.6097 − 0.1826i
W21	−0.5000	0.5000i	0.5000	−0.5000i
W22	−0.2570 − 0.1701i	−0.1826 + 0.6097i	0.2570 − 0.1701i	−0.1826 − 0.6097i
W23	−0.3527 + 0.4396i	0.4271	−0.3527 − 0.4396i	−0.4271
W24	0.1701 − 0.2570i	−0.6097 + 0.1826i	0.1701 + 0.2570i	0.6097 + 0.1826i
W25	0.5000	0.5000	0.5000	0.5000
W26	0.6097 + 0.1826i	0.2570 − 0.1826i	0.2570 − 0.1701i	0.6097 + 0.1701i
W27	−0.4271i	0.1826 − 0.2570i	−0.3527 − 0.4396i	0.1701 − 0.6097i
W28	0.1826 + 0.6097i	0.4396i	0.1701 + 0.2570i	−0.3527 + 0.4271i
W29	0.5000	0.5000i	0.5000	0.5000i
W30	0.6097 + 0.1826i	−0.1701 + 0.6097i	0.2570 − 0.1701i	0.1826 + 0.2570i
W31	−0.4271i	0.6097 + 0.1701i	−0.3527 − 0.4396i	0.2570 + 0.1826i
W32	0.1826 + 0.6097i	−0.4271 − 0.3527i	0.1701 + 0.2570i	−0.4396
W33	0.5000	0.5000	0.5000	−0.5000
W34	0.2570 − 0.1701i	0.4396	0.6097 − 0.1826i	−0.4271 − 0.3527i
W35	−0.3527 − 0.4396i	0.1826 − 0.2570i	−0.4271i	−0.1701 + 0.6097i
W36	0.1701 + 0.2570i	0.1826 + 0.2570i	−0.1826 + 0.6097i	0.1701 − 0.6097i
W37	0.5000	−0.5000i	−0.5000	−0.5000i
W38	0.2570 − 0.1701i	−0.4396i	−0.6097 + 0.1826i	0.3527 − 0.4271i
W39	−0.3527 − 0.4396i	−0.2570 − 0.1826i	0.4271i	−0.6097 − 0.1701i
W40	0.1701 + 0.2570i	0.2570 − 0.1826i	0.1826 − 0.6097i	0.6097 + 0.1701i
W41	0.5000	−0.5000	0.5000	0.5000
W42	0.2570 − 0.1701i	−0.4396	0.6097 − 0.1826i	0.4271 + 0.3527i
W43	−0.3527 − 0.4396i	−0.1826 + 0.2570i	−0.4271i	0.1701 − 0.6097i
W44	0.1701 + 0.2570i	−0.1826 − 0.2570i	−0.1826 + 0.6097i	−0.1701 + 0.6097i
W45	0.5000	0.5000i	−0.5000	0.5000i
W46	0.2570 − 0.1701i	0.4396i	−0.6097 + 0.1826i	−0.3527 + 0.4271i
W47	−0.3527 − 0.4396i	0.2570 + 0.1826i	0.4271i	0.6097 + 0.1701i
W48	0.1701 + 0.2570i	−0.2570 + 0.1826i	0.1826 − 0.6097i	−0.6097 − 0.1701i
W49	0.5000	0.3536 + 0.3536i	0.5000i	−0.3536 + 0.3536i
W50	0.2570 − 0.1701i	0.3108 + 0.3108i	0.1826 + 0.6097i	−0.5514 + 0.0526i
W51	−0.3527 − 0.4396i	0.3108 − 0.0526i	0.4271	0.3108 + 0.5514i
W52	0.1701 + 0.2570i	−0.0526 + 0.3108i	−0.6097 − 0.1826i	−0.3108 − 0.5514i
W53	0.5000	0.3536 − 0.3536i	−0.5000i	−0.3536 − 0.3536i
W54	0.2570 − 0.1701i	0.3108 − 0.3108i	−0.1826 − 0.6097i	−0.0526 − 0.5514i
W55	−0.3527 − 0.4396i	−0.0526 − 0.3108i	−0.4271	−0.5514 + 0.3108i
W56	0.1701 + 0.2570i	0.3108 + 0.0526i	0.6097 + 0.1826i	0.5514 − 0.3108i
W57	0.5000	−0.3536 − 0.3536i	0.5000i	0.3536 − 0.3536i
W58	0.2570 − 0.1701i	−0.3108 − 0.3108i	0.1826 + 0.6097i	0.5514 − 0.0526i
W59	−0.3527 − 0.4396i	−0.3108 + 0.0526i	0.4271	−0.3108 − 0.5514i
W60	0.1701 + 0.2570i	0.0526 − 0.3108i	−0.6097 − 0.1826i	0.3108 + 0.5514i
W61	0.5000	−0.3536 + 0.3536i	−0.5000i	0.3536 + 0.3536i
W62	0.2570 − 0.1701i	−0.3108 + 0.3108i	−0.1826 − 0.6097i	0.0526 + 0.5514i
W63	−0.3527 − 0.4396i	0.0526 + 0.3108i	−0.4271	0.5514 − 0.3108i
W64	0.1701 + 0.2570i	−0.3108 − 0.0526i	0.6097 + 0.1826i	−0.5514 + 0.3108i

Although the embodiments and their advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims. Moreover, the scope of the present application is not intended to be limited to the particular embodiments of the process, machine, manufacture, composition of matter, means, methods and steps described in the specification. As one of ordinary skill in the art will readily appreciate from the disclosure of the present invention, processes, machines, manufacture, compositions of matter, means, methods, or steps, presently existing or later to be developed, that perform substantially the same function or achieve substantially the same result as the corresponding embodiments described herein may be utilized according to the present invention. Accordingly, the appended claims are intended to include within their scope such processes, machines, manufacture, compositions of matter, means, methods, or steps.

Claims (23)

What is claimed is:

1. A method for communications device operation, the method comprising:

estimating a communications channel between the communications device and a controller serving the communications device, thereby producing a channel estimate;

quantizing the channel estimate using a codebook, wherein the codebook comprises a plurality of first level codewords, and wherein each first level codeword has a plurality of subsidiary codewords, thereby producing a selected codeword; and

transmitting an index corresponding to the selected codeword from the codebook to the controller,

wherein quantizing the channel estimate using a codebook comprises:

selecting a first level codeword from the plurality of first level codewords that maximizes |HW_i|, iε[1, . . . , # first level codewords], where H is a channel matrix, and W_iare codewords of codebook, and # first level codewords is the number of first level codewords in the plurality of first level codewords;

selecting a subsidiary codeword from the plurality of subsidiary codewords of the first level codeword that maximizes |HW_i|, iε[1, . . . , # subsidiary codewords], where # subsidiary codewords is the number of subsidiary codewords of the first level codeword; and

selecting either the first level codeword or the subsidiary codeword based on which codeword maximizes |HW_i|, iε[the first codeword, the subsidiary codeword] as the selected codeword.

2. The method ofclaim 1, wherein selecting either the first level codeword or the subsidiary codeword comprises selecting the first level codeword in response to determining that the first level codeword and the subsidiary codeword substantially equally maximizes |HW_i|, iε[the first codeword, the subsidiary codeword].

3. The method ofclaim 1, wherein selecting either the first level codeword or the subsidiary codeword comprises randomly selecting either the first level codeword or the subsidiary codeword in response to determining the first level codeword and the subsidiary codeword substantially equally maximizes |HW_i|, iε[the first codeword, the subsidiary codeword].

4. The method ofclaim 1, wherein the communications device comprises four transmit antennas, and wherein the codebook is expressible as:

W=D×[W₁; . . . ;W₆₄],

where D is the phase rotation diagonal matrix and given by

$D=\left[\begin{array}{cccc}{e}^{j{\theta }_1}& 0& \dots & 0\\ 0& e^{j{\theta }_2}& \ddots & ⋮\\ ⋮& \ddots & \ddots & 0\\ 0& \dots & 0& e^{j{\theta }_{64}}\end{array}\right],$

where θ_iε[0,2π), iε[1, . . . , 64].

5. The method ofclaim 1, wherein the number of subsidiary codewords in each plurality of subsidiary codewords is equal.

6. A method for communications device operation, the method comprising:

estimating a communications channel between the communications device and a controller serving the communications device, thereby producing a channel estimate;

quantizing the channel estimate using a codebook, wherein the codebook comprises a plurality of first level codewords, and wherein each first level codeword has a plurality of subsidiary codewords, thereby producing a selected codeword; and

transmitting an index corresponding to the selected codeword from the codebook to the controller,

wherein the communications device comprises four transmit antennas,

wherein the codebook is expressible as: W=D×[W₁; . . . ; W₆₄],

where D is the phase rotation diagonal matrix and given by

$D=\left[\begin{array}{cccc}{e}^{j{\theta }_1}& 0& \dots & 0\\ 0& e^{j{\theta }_2}& \ddots & ⋮\\ ⋮& \ddots & \ddots & 0\\ 0& \dots & 0& e^{j{\theta }_{64}}\end{array}\right],$

where θ_iε[0,2π), iε[1, . . . , 64], and

wherein a codeword in the codebook is expressible as:

W_4i+j=U_iK^Hz_j, iε[0, . . . ,15], jε[1, . . . ,4],

where Z=[z₁, z₂, z₃, z₄] and K=[z₁, k₂, k₃, k₄] are two 4×4 unitary matrices, z_jis the j-th column of Z, matrices Z and K do not have to be identical, C=[c₁, . . . , c₁₆] is a 4×16 matrix, c_i, iε[1, . . . , 16] is 4×1 vector, and U_iis a 4×4 unitary matrix denoted by U_i=[c_i, u_i2, u_i3, u_i4].

7. The method ofclaim 6, wherein matrix C is specified as follows:

c₁0.5000−0.50000.5000−0.5000c₂−0.5000−0.50000.50000.5000c₃−0.50000.50000.5000−0.5000c₄0.5000−0.5000I0.5000−0.5000Ic₅−0.5000−0.5000I0.50000.5000Ic₆−0.50000.5000I0.5000−0.5000Ic₇0.50000.50000.5000−0.5000c₈0.5000−0.5000I−0.5000−0.5000Ic₉0.5000−0.50000.50000.5000c₁₀0.50000.5000I−0.50000.5000Ic₁₁0.5000 0.3536 + 0.3536I0.5000I−0.3536 + 0.3536Ic₁₂0.5000 0.3536 − 0.3536I−0.5000I−0.3536 − 0.3536Ic₁₃0.5000−0.3536 − 0.3536I0.5000I 0.3536 − 0.3536Ic₁₄0.5000−0.3536 + 0.3536I−0.5000I 0.3536 + 0.3536Ic₁₅0.50000.50000.50000.5000c₁₆0.50000.5000I0.50000.5000I

8. The method ofclaim 6, wherein matrices Z and K are specified as follows:

$Z=K=\left[\begin{array}{cccc}-0.5& -0.5& 0.5j& -0.5j\\ 0.5j& 0.5j& -0.5& 0.5\\ 0.5j& -0.5j& -0.5& -0.5\\ 0.5& -0.5& -0.5j& -0.5j\end{array}\right].$

9. The method ofclaim 6, wherein matrix U is specified as follows:

$\begin{array}{c}{U}_1=\left[\begin{array}{cccc}0.5& -0.5& -0.5& 0.5\\ -0.5& -0.5& 0.5& 0.5\\ 0.5& 0.5& 0.5& 0.5\\ -0.5& 0.5& -0.5& 0.5\end{array}\right]\\ U_2=\left[\begin{array}{cccc}-0.5& -0.5& 0.5& 0.5\\ -0.5& 0.5& 0.5& -0.5\\ 0.5& 0.5& 0.5& 0.5\\ 0.5& -0.5& 0.5& -0.5\end{array}\right]\\ U_3=\left[\begin{array}{cccc}-0.5& 0.5& 0.5& -0.5\\ 0.5& 0.5& -0.5& -0.5\\ 0.5& 0.5& 0.5& 0.5\\ -0.5& 0.5& -0.5& 0.5\end{array}\right]\\ U_4=\left[\begin{array}{cccc}0.5& -0.5& -0.5& 0.5\\ -0.5j& -0.5j& 0.5j& 0.5j\\ 0.5& 0.5& 0.5& 0.5\\ -0.5j& 0.5j& -0.5j& 0.5j\end{array}\right]\\ U_5=\left[\begin{array}{cccc}-0.5& -0.5& 0.5& 0.5\\ -0.5j& 0.5j& 0.5j& -0.5j\\ 0.5& 0.5& 0.5& 0.5\\ 0.5j& -0.5j& 0.5j& -0.5j\end{array}\right]\\ U_6=\left[\begin{array}{cccc}-0.5& 0.5& 0.5& -0.5\\ 0.5j& 0.5j& -0.5j& -0.5j\\ 0.5& 0.5& 0.5& 0.5\\ -0.5j& 0.5j& -0.5j& 0.5j\end{array}\right]\\ U_7=\left[\begin{array}{cccc}0.5& 0.5& -0.5& -0.5\\ 0.5& -0.5& -0.5j& 0.5j\\ 0.5& 0.5& 0.5& 0.5\\ 0.5& -0.5& 0.5j& -0.5j\end{array}\right]\\ U_8=\left[\begin{array}{cccc}0.5& 0.5& -0.5& -0.5\\ 0.5j& -0.5j& -0.5& 0.5\\ 0.5& 0.5& 0.5& 0.5\\ 0.5j& -0.5j& 0.5& -0.5\end{array}\right]\\ U_9=\left[\begin{array}{cccc}0.5& 0.5& 0.5& 0.5\\ 0.5& -0.5j& -0.5& 0.5j\\ 0.5& -0.5& 0.5& -0.5\\ -0.5& -0.5j& 0.5& 0.5j\end{array}\right]\\ U_{10}=\left[\begin{array}{cccc}0.5& 0.5& 0.5& 0.5\\ -0.5j& -0.5& 0.5j& 0.5\\ -0.5& 0.5& -0.5& 0.5\\ -0.5j& 0.5& 0.5j& -0.5\end{array}\right]\\ U_{11}=\left[\begin{array}{cccc}0.5& 0.5& 0.5& 0.5\\ -0.5& 0.5j& 0.5& -0.5j\\ 0.5& -0.5& 0.5& -0.5\\ 0.5& 0.5j& -0.5& -0.5j\end{array}\right]\\ U_{12}=\left[\begin{array}{cccc}0.5& 0.5& 0.5& 0.5\\ 0.5j& 0.5& -0.5j& -0.5\\ -0.5& 0.5& -0.5& 0.5\\ 0.5j& -0.5& -0.5j& 0.5\end{array}\right]\\ U_{13}=\left[\begin{array}{cccc}0.5& 0.5& 0.5& 0.5\\ \sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j\\ 0.5j& -0.5j& 0.5j& -0.5j\\ -\sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j\end{array}\right]\\ U_{14}=\left[\begin{array}{cccc}0.5& 0.5& 0.5& 0.5\\ \sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j\\ -0.5j& 0.5j& -0.5j& 0.5j\\ -\sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j\end{array}\right]\\ U_{15}=\left[\begin{array}{cccc}0.5& 0.5& 0.5& 0.5\\ -\sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j\\ 0.5j& -0.5j& 0.5j& -0.5j\\ \sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j\end{array}\right]\\ U_{16}=\left[\begin{array}{cccc}0.5& 0.5& 0.5& 0.5\\ -\sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j\\ -0.5j& 0.5j& -0.5j& 0.5j\\ \sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}+\sqrt{\frac{1}{8}}j& -\sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j& \sqrt{\frac{1}{8}}-\sqrt{\frac{1}{8}}j\end{array}\right].\end{array}$

10. The method ofclaim 6, wherein the codewords [W₁, . . . , W₆₄] of the codebook W with four place precision are expressible as:

W₁0.5000−0.50000.5000−0.5000W₂0.2570 + 0.1701i−0.6097 − 0.1826i 0.2570 − 0.1701i−0.6097 + 0.1826i W₃0.3527 − 0.4396i0.4271i−0.3527 − 0.4396i    0 + 0.4271iW₄−0.1701 + 0.2570i −0.1826 − 0.6097i 0.1701 + 0.2570i0.1826 − 0.6097iW₅−0.5000−0.50000.50000.5000W₆−0.6097 − 0.1826i −0.2570 − 0.1701i 0.2570 − 0.1701i0.6097 − 0.1826iW₇   0 + 0.4271i−0.3527 + 0.4396i −0.3527 − 0.4396i −0.4271iW₈−0.1826 − 0.6097i 0.1701 − 0.2570i0.1701 + 0.2570i−0.1826 + 0.6097i W₉−0.50000.50000.5000−0.5000W₁₀−0.2570 − 0.1701i 0.6097 + 0.1826i0.2570 − 0.1701i−0.6097 + 0.1826i W₁₁−0.3527 + 0.4396i 0 − 0.4271i−0.3527 − 0.4396i 0.4271iW₁₂0.1701 − 0.2570i0.1826 + 0.6097i0.1701 + 0.2570i0.1826 − 0.6097iW₁₃0.5000−0.5000i0.5000−0.5000iW₁₄0.2570 + 0.1701i0.1826 − 0.6097i0.2570 − 0.1701i−0.1826 − 0.6097i W₁₅0.3527 − 0.4396i−0.4271−0.3527 − 0.4396i −0.4271W₁₆−0.1701 + 0.2570i 0.6097 − 0.1826i0.1701 + 0.2570i0.6097 + 0.1826iW₁₇−0.5000−0.5000i0.50000.5000iW₁₈−0.6097 − 0.1826i 0.1701 − 0.2570i0.2570 − 0.1701i0.1826 − 0.6097iW₁₉0.4271i−0.4396 − 0.3527i −0.3527 − 0.4396i 0.4271W₂₀−0.1826 − 0.6097i 0.2570 + 0.1701i0.1701 + 0.2570i−0.6097 − 0.1826i W₂₁−0.50000.5000i0.5000−0.5000iW₂₂−0.2570 − 0.1701i −0.1826 + 0.6097i 0.2570 − 0.1701i−0.1826 − 0.6097i W₂₃−0.3527 + 0.4396i 0.4271−0.3527 − 0.4396i −0.4271W₂₄0.1701 − 0.2570i−0.6097 + 0.1826i 0.1701 + 0.2570i0.6097 + 0.1826iW₂₅0.50000.50000.50000.5000W₂₆0.6097 + 0.1826i0.2570 − 0.1826i0.2570 − 0.1701i0.6097 + 0.1701iW₂₇−0.4271i0.1826 − 0.2570i−0.3527 − 0.4396i 0.1701 − 0.6097iW₂₈0.1826 + 0.6097i0.4396i0.1701 + 0.2570i−0.3527 + 0.4271i W₂₉0.50000.5000i0.50000.5000iW₃₀0.6097 + 0.1826i−0.1701 + 0.6097i 0.2570 − 0.1701i0.1826 + 0.2570iW₃₁−0.4271i0.6097 + 0.1701i−0.3527 − 0.4396i 0.2570 + 0.1826iW₃₂0.1826 + 0.6097i−0.4271 − 0.3527i 0.1701 + 0.2570i−0.4396W₃₃0.50000.50000.5000−0.5000W₃₄0.2570 − 0.1701i0.43960.6097 − 0.1826i−0.4271 − 0.3527i W₃₅−0.3527 − 0.4396i 0.1826 − 0.2570i−0.4271i−0.1701 + 0.6097i W₃₆0.1701 + 0.2570i0.1826 + 0.2570i−0.1826 + 0.6097i 0.1701 − 0.6097iW₃₇0.5000−0.5000i−0.5000−0.5000iW₃₈0.2570 − 0.1701i−0.4396i−0.6097 + 0.1826i 0.3527 − 0.4271iW₃₉−0.3527 − 0.4396i −0.2570 − 0.1826i 0.4271i−0.6097 − 0.1701i W₄₀0.1701 + 0.2570i0.2570 − 0.1826i0.1826 − 0.6097i0.6097 + 0.1701iW₄₁0.5000−0.50000.50000.5000W₄₂0.2570 − 0.1701i−0.43960.6097 − 0.1826i0.4271 + 0.3527iW₄₃−0.3527 − 0.4396i −0.1826 + 0.2570i −0.4271i0.1701 − 0.6097iW₄₄0.1701 + 0.2570i−0.1826 − 0.2570i −0.1826 + 0.6097i −0.1701 + 0.6097i W₄₅0.50000.5000i−0.50000.5000iW₄₆0.2570 − 0.1701i0.4396i−0.6097 + 0.1826i −0.3527 + 0.4271i W₄₇−0.3527 − 0.4396i 0.2570 + 0.1826i0.4271i0.6097 + 0.1701iW₄₈0.1701 + 0.2570i−0.2570 + 0.1826i 0.1826 − 0.6097i−0.6097 − 0.1701i W₄₉0.50000.3536 + 0.3536i0.5000i−0.3536 + 0.3536i W₅₀0.2570 − 0.1701i0.3108 + 0.3108i0.1826 + 0.6097i−0.5514 + 0.0526i W₅₁−0.3527 − 0.4396i 0.3108 − 0.0526i0.42710.3108 + 0.5514iW₅₂0.1701 + 0.2570i−0.0526 + 0.3108i −0.6097 − 0.1826i −0.3108 − 0.5514i W₅₃0.50000.3536 − 0.3536i−0.5000i−0.3536 − 0.3536i W₅₄0.2570 − 0.1701i0.3108 − 0.3108i−0.1826 − 0.6097i −0.0526 − 0.5514i W₅₅−0.3527 − 0.4396i −0.0526 − 0.3108i −0.4271−0.5514 + 0.3108i W₅₆0.1701 + 0.2570i0.3108 + 0.0526i0.6097 + 0.1826i0.5514 − 0.3108iW₅₇0.5000−0.3536 − 0.3536i 0.5000i0.3536 − 0.3536iW₅₈0.2570 − 0.1701i−0.3108 − 0.3108i 0.1826 + 0.6097i0.5514 − 0.0526iW₅₉−0.3527 − 0.4396i −0.3108 + 0.0526i 0.4271−0.3108 − 0.5514i W₆₀0.1701 + 0.2570i0.0526 − 0.3108i−0.6097 − 0.1826i 0.3108 + 0.5514iW₆₁0.5000−0.3536 + 0.3536i −0.5000i0.3536 + 0.3536iW₆₂0.2570 − 0.1701i−0.3108 + 0.3108i −0.1826 − 0.6097i 0.0526 + 0.5514iW₆₃−0.3527 − 0.4396i 0.0526 + 0.3108i−0.427i0.5514 − 0.3108iW₆₄0.1701 + 0.2570i−0.3108 − 0.0526i 0.6097 + 0.1826i−0.5514 + 0.3108i 

11. A method for communications device operation, the method comprising:

estimating a communications channel between the communications device and a controller serving the communications device, thereby producing a channel estimate;

performing a first stage quantization of the channel estimate using a codebook, wherein the codebook comprises a plurality of first level codewords, wherein each first level codeword has a plurality of subsidiary codewords, and wherein the first stage quantization uses only the plurality of first level codewords, thereby producing a selected first level codeword;

transmitting a first index corresponding to the selected first level codeword from the codebook to the controller;

performing a second stage quantization of the channel estimate using the codebook, wherein the second stage quantization uses the entirety of the codebook, thereby producing a selected codeword; and

transmitting a second index corresponding to the selected codeword from the codebook to the controller,

wherein performing a first stage quantization of the channel estimate comprises, selecting a first level codeword from the plurality of first level codewords that maximizes |HW_i|, iε[1, . . . , # first level codewords] as the selected first level codeword, where H is a channel matrix, and W_iare codewords of codebook, and # first level codewords is the number of first level codewords in the plurality of first level codewords.

12. A method for communications device operation, the method comprising:

estimating a communications channel between the communications device and a controller serving the communications device, thereby producing a channel estimate;

performing a first stage quantization of the channel estimate using a codebook, wherein the codebook comprises a plurality of first level codewords, wherein each first level codeword has a plurality of subsidiary codewords, and wherein the first stage quantization uses only the plurality of first level codewords, thereby producing a selected first level codeword;

transmitting a first index corresponding to the selected first level codeword from the codebook to the controller;

performing a second stage quantization of the channel estimate using the codebook, wherein the second stage quantization uses the entirety of the codebook, thereby producing a selected codeword; and

transmitting a second index corresponding to the selected codeword from the codebook to the controller,

wherein performing a second stage quantization of the channel estimate comprises:

selecting a subsidiary codeword from the plurality of subsidiary codewords of the selected first level codeword that maximizes |HW_i|, iε[1, . . . , # subsidiary codewords], where H is a channel matrix, and W_iare codewords of codebook, and # subsidiary codewords is the number of subsidiary codewords of the first level codeword; and

selecting either the selected first level codeword or the subsidiary codeword based on which codeword maximizes |HW_i|, iε[the first codeword, the subsidiary codeword] as the selected codeword.

13. The method ofclaim 12, wherein selecting either the selected first level codeword or the subsidiary codeword comprises, selecting the selected first level codeword in response to determining that the first level codeword and the subsidiary codeword substantially equally maximizes |HW_i|, iε[the first codeword, the subsidiary codeword].

14. The method ofclaim 12, further comprising, normalizing the channel estimate prior to performing a first stage quantization of the channel estimate.

15. A method for controller operation, the method comprising:

receiving a first channel state information (CSI) from a communications device, wherein the first CSI comprises a first index to a first level codeword in a codebook, wherein the codebook comprises a plurality of first level codewords, wherein each first level codeword has a plurality of subsidiary codewords;

reconstructing a first channel estimate using the codebook and the first index;

adjusting transmission circuitry in the controller using the reconstructed first channel estimate; and

receiving a second CSI from a communications device, wherein the second CSI comprises a second index to a codeword in the codebook;

wherein in response to determining that the first index is different from the second index, the method further comprises:

reconstructing a second channel estimate using the codebook and the second index,

adjusting transmission circuitry in the controller using the reconstructed second channel estimate;

transmitting a first transmission to the communications device using the adjusted transmission circuitry, wherein transmitting the first transmission comprises:

in response to determining that the first index is not different from the second index, precoding the transmission with the reconstructed first channel estimate, thereby producing a first precoded transmission, and transmitting the first precoded transmission to the communications device; and

in response to determining that the first index is different from the second index, precoding the transmission with the reconstructed second channel estimate, thereby producing a second precoded transmission, and transmitting the second precoded transmission to the communications device.

16. The method ofclaim 15, further comprising, prior to receiving a second CSI, transmitting a second transmission to the communications device.

17. The method ofclaim 15, wherein the first CSI is encoded in a message from the communications device, and wherein receiving a first CSI comprises:

receiving the first CSI; and

decoding the first CSI to extract the first index.

18. A communications device comprising:

a processor; and

a computer readable storage medium storing programming for execution by the processor, the programming including instructions to:

perform channel estimation on a communications channel between the communications device and a controller serving the communications device to produce a channel estimate;

quantize the channel estimate using a codebook to produce a selected codeword, wherein the codebook comprises a plurality of first level codewords and a plurality of subsidiary codewords, and wherein each first level codeword corresponds to a unique sub-set of the plurality of subsidiary codewords, wherein fewer than all of the plurality of subsidiary codewords are included in the unique sub-set of subsidiary codewords corresponding to the optimal first level codeword, and wherein none of the plurality of first level codewords are subsidiary codewords; and

transmit an index corresponding to the selected codeword from the codebook to the controller.

19. The communications device ofclaim 18, wherein the instructions to quantize the channel estimate include instructions to:

analyze the plurality of first level codewords to identify an optimal one of the plurality of first level codewords;

analyze each subsidiary codeword in the unique sub-set of subsidiary codewords that corresponds to the optimal first level codeword to identify an optimal subsidiary codeword, wherein subsidiary codewords in the plurality of subsidiary codewords that are not included in the unique sub-set of subsidiary codewords corresponding to the optimal first level codeword are not analyzed during said quantization; and

pursuant to said analysis, select one of the optimal first level codeword or the optimal subsidiary codeword as the selected codeword.

20. A communications device for performing quantization using a codebook that includes a plurality of first level codewords and a plurality of subsidiary codewords, the communications device comprising:

a processor; and

a computer readable storage medium storing programming for execution by the processor, the programming including instructions to:

estimate a communications channel between the communications device and a controller serving the communications device to produce a channel estimate;

perform a first stage quantization of the channel estimate to identify an optimal one of the plurality of first level codewords;

transmit a first indication that identifies the optimal first level codeword;

subsequent to transmitting the first indication, perform a second stage quantization of the channel estimate to identify an optimal codeword; and

transmit a second indication that identifies the optimal codeword,

wherein each of the plurality of first level codewords corresponds to a unique sub-set of the plurality of subsidiary codewords, and

wherein the instructions to perform the second stage quantization include instructions to analyze each subsidiary codeword in the unique sub-set of subsidiary codewords corresponding to the optimal first level codeword without analyzing ones of the plurality of subsidiary codewords that are not in the unique sub-set of subsidiary codewords corresponding to the optimal first level codeword.

21. The communications device ofclaim 20, wherein the instructions to perform the first stage quantization include instructions to analyze each of the plurality of first level codewords without analyzing any of the subsidiary codewords.

22. The communications device ofclaim 21, wherein the instructions to perform the second stage quantization include instructions to analyze at least some of the plurality of subsidiary codewords.

23. The communications device ofclaim 20, wherein fewer than all of the plurality of subsidiary codewords are included in the unique sub-set of subsidiary codewords corresponding to the optimal first level codeword, and wherein none of the first level codewords are subsidiary codewords.

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